Cut the chickens into halves lenthways, pull and discard the rib bones. Brown (for 10 to 15 minutes) with 2 tablespoons of the chosen fat in a high-sided frying pan, take the pieces out, keep warm. Add 2 more tablespoons of fat to their frying fat and juice, gently fry the finely sliced onions, over a very moderate heat (20 minutes). When browned, put in the chickens again, salt, pepper, add 1 branch of thyme and 1 bay leaf. Cover, finish the cooking, stirring from time to time to prevent the onions from burning. Serve with French fries or potato chips.